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1、CHAPTER 7Continuous Probability Distributionsto accompanyIntroduction to Business Statisticsfourth edition,by Ronald M.WeiersPresentation by Priscilla Chaffe-Stengel Donald N.Stengel 2002 The Wadsworth GroupChapter 7-Learning ObjectivesDifferentiate between the normal and the exponential distributio
2、ns.Use the standard normal distribution and z-scores to determine probabilities associated with the normal distribution.Use the normal distribution to approximate the binomial distribution.Use the exponential distribution to determine related probabilities.2002 The Wadsworth GroupChapter 7-Key Terms
3、Probability density functionProbability distributionsStandard normal distributionMean,variance,applicationsExponential distributionMean,variance,applicationsNormal approximation to the binomial distribution 2002 The Wadsworth GroupChapter 7-Key ConceptThe area under a probability density function be
4、tween two bounds,a and b,is the probability that a value will occur within the bounded interval between a and b.2002 The Wadsworth GroupAreas under the Normal CurveUse the standard normal table to find:The z-score such that the area from the midpoint to z is 0.20.In the interior of the standard norm
5、al table,look up a value close to 0.20.The closest value is 0.1985,which occurs at z=0.52.2002 The Wadsworth GroupAreas under the Normal CurveUse the standard normal table to find:The probability associated with z:P(0 z 1.32).Locate the row whose header is 1.3.Proceed along that row to the column wh
6、ose header is.02.There you find the value.4066,which is the amount of area capture between the mean and a z of 1.32.Answer:0.4066 2002 The Wadsworth GroupAreas under the Normal CurveUse the standard normal table to find:The probability associated with z:P(1.10 z 1.32).Find the amount of area between
7、 the mean and z=1.32 and add it to the amount of area between the mean and z=1.10*.0.3643+0.4066=0.7709 2002 The Wadsworth GroupAreas under the Normal CurveUse the standard normal table to find:The probability associated with z:P(1.00 z 1.32).Find the amount of area between the mean and z=1.00 and s
8、ubtract it from the amount of area between the mean and z=1.32.0.4066 0.3413=0.0653 2002 The Wadsworth GroupStandardizing Individual Data Values on a Normal CurveThe standardized z-score is how far above or below the individual value is compared to the population mean in units of standard deviation.
9、“How far above or below”=data value mean“In units of standard deviation”=divide by sStandardized individual value 2002 The Wadsworth GroupAn Example,cont.Given in the problem:=12.1 minutes,s=2.0 minutesa)Greater than 14.1 minutesP(x 14.1)=P(z 1.00)=.5 .3413=0.1587z=xms=14.112.12.0=1.00 2002 The Wads
10、worth GroupAn Example,cont.Given in the problem:=12.1 minutes,s=2.0 minutesc)Between 10.1 and 14.1 minutesP(10.1 x 14.1)=P(1.00 z 1.00)=0.3413+0.3413=0.6826zlower=xms=10.112.12.0=1.00zupper=xms=14.112.12.0=1.00 2002 The Wadsworth GroupAn Example,cont.Given in the problem:=12.1 minutes,s=2.0 minutesd
11、)Between 10.1 and 16.1 minutesP(10.1 x 16.1)=P(1.00 z 2.00)=0.3413+0.4772=0.8185 2002 The Wadsworth GroupExample:Using Microsoft ExcelProblem:What is the probability that the time required for Mary and her bags to get to the room will be:c)between 10.1 and 14.1 minutes?In a cell on an Excel workshee
12、t,type all on one line=NORMDIST(14.1,12.1,2,true)-NORMDIST(10.1,12.1,2,true)and you will see the answer:0.6826d)between 10.1 and 16.1 minutes?In a cell on an Excel worksheet,type all on one line=NORMDIST(16.1,12.1,2,true)-NORMDIST(10.1,12.1,2,true)and you will see the answer:0.8185 2002 The Wadswort
13、h GroupThe Exponential Distribution where l=mean and standard deviation e=2.71828,a constantProbability:Application:Every day,drivers arrive at a tollbooth.If the Poisson distribution were applied to this process,what would be an appropriate random variable?What would be the exponential distribution counterpart to this random variable?2002 The Wadsworth Group